MUKHERJEE, KELLY, RICHARDR, AND LUKACS
580 ether. This is based on the fact that the changes observed in the infrared for chlorophyll b in ethyl ether did not occur in chloroform even when the mole ratio of trinitrobenzene to chlorophyll b was 18:l. Consequently, a sufficient amount of complex is not present for the nnir runs of chlorophyll b in order to gain much information about the system. There obviously is some complexing since the proton resonance of trinitrobenzene is shifted about 60 cycles to higher fields indicating it is within the diamagnetic shielding zone of the chlorophyll ring. Also there is a considerable paramagnetic shift of the phytyl oxygen bonded methyleiie group. The only proton which experiences n diamagnetic shift is the cy proton. It seems likely that the system here would be quite similar to the chloropliyll a complex. The shift of methylene protons is again inlerpreled its arising from displacement of the hydrocarbon tail from the region of the ring by trinitrobenzene The conclusion that chnrge-transfer interacl ion occurs in the vicinity of the cy and 0 protons of lhe chlorophyll molecule is in disagreement with some of the current opinions which regard the cyclopentanone region (ring V) an important center of high electron density. However, it seems quite logical that the area of the chlorophyll molecule which will be involved in electron donation will depend on the environment in which the molecule is placed. It is very likely that solvent perturbations will be a major factor in determining this region. Furthermore, steric considerations with the
acceptor molecule must not be neglected. This may be a contributing factor in the present situation. If the hydrocarbon tail is preferentially oriented in such a way that it is within the vicinity of the porphyrin head as ninr results imply, then perhaps large molecules, such as trinitrobenzene, must interact with the upper part of the chlorophyll molecule where steric interactions with the tail are minimized. Obviously it would be of interest to investigate systems like the one presented here or else similar ones in various solvent systems. A systematic s t j d y of this type could reveal what role solvent plays in influencing the site of electron donation. Nelson13has investigated the electronic energy levels in chlorophyll derivatives. He found values of 4.03 eV for ethyl chlorophyllide a and 5.16 eV for ethylchlorophyllide b. This means that ethyl chlorophyllide a is a better electron donor than ethyl chlorophyllide b in the solid film. If solvent effects are small, the binding constants for TNB in ether should be larger for chlorophj7ll a than for chlorophyll b. This is what is observed here. A quantitative correlation has not been made.
Acknowledgments. This research has been generously supported by grants from the National Science Foundation (GB2254) and the Kational Institutes of Health (5R01 GM10856-06). (13) R. 0.Nelson, Photochem. PhotobioL, 8 ( 5 ) , 441 (1968).
Equilibria in Pyridine. 11. Behavior of Some Monovalent Silver Salts in Pyridine by L. M. Mukherjee, J. J. Kelly, McDonald Richards, and J. M. Lukacs, Jr. Chemistry Department, Polytechnic Institute of Brooklyn, Brooklyn, New York 11801
(ReceCed August 1, 1908)
The cell Zn(Hg)IZnClz(s)lIAgXin pyridinelAg(s) has been used to study the behavior of the nitrate, picrate, chloride, cyanide, and thiocyanate of silver(1). Correlating the potentiometric behavior with the conductance data for these differentsilver salts eventually made possible the evaluation of the standard potential of the reso obtained is 0.551 V vs. a nornial hydrogen action Ag(so1v)+ e Ag(s) in pyridine, The value of electrode at 25'.
+
*
Introduction In this work a silver indicator electrode has been used to study the behavior of silver nitrate, picrate, chloride, cyanide, and thiocyanate in pyridine, in conjunction with a Zn(Hg) 1ZnC12(s) reference electrode' which has previously been standardized against a normal hydrogen electrode (nhe). Correlation of these potentiometric results with earlier conductance studies2i3eventually provided the value of the standard potential of The Journal of Physical Chemistry
the reaction
+
Ag(solv)+ e E Ag(s) (1) in pyridine. I n the'case of silver nitratJe and picrate, (1) (a) L. M. Mukherjee and J. J. Kelly, J Phys. Chem., 71, 2348 (1967); (b) L. M. Mukherjee, J. *J, Kelly, W. BnranetBlcy, and 4J. Sica, i b i d . , 72, 3410 (1908). (2) (a) W. F. Luder and C. A. Kraus, J . Ana. Chem. Soc., 69, 2481 (1947); (b) I). S. Burgess and C. A . Kmus, ibid., 70, 70G (1948). (3) J. H . Mathews and A. J. Johnson, J . Phys. Ckem., 2 1 , 294 (1916-1917).
EQUILIBRIA IN PYRIDINE
581
use has been made of the dissociation constants reported by Kraus, et al.2 However, although the previously reported conductance studies for the chloride, cyanide, and thiocyanate strongly suggest the possible existence of a substantial degree of ion association, no quantitative estimates of the equilibrium constants for these systems are available. Therefore, before any correlation with the potentiometric results in these cases could be attempted, it became necessary to explain their conductance data3 on the basis of typical equilibria involving simple ions and triple ions as well as quadrupoles (“dimers”). We used a simple trial and error procedure in this connection until a satisfactory agreement with the observed conductances was obtained. The trial values of these different parameters which yielded the best fit have subsequently been incorporated in the potentiometric results.
Theory
Combining eq 8 with eq 7b, one obtains CAgX = [Ag+l
+ [&XI + 3 [AgzX+l + 2 [Ag2X21
Now, expressing [AgX], [Ag,X+], and [Ag2X2] in terms of [Ag+] according to eq 2, 3a, 3b, 4a, and 4b and equating K2&,K2b, and K2 as before and setting Kaa = KSb = K3, we obtain CAgX = [Ag+l+ KI [&+Iz
+ 3KiKz[Ag+13+ 2KXzK3 [Ag+14 (10)
According to eq 10, for any assumed values of [Ag+], K1, Kz, and Ks, the corresponding value of C A ~can X be calculated. Calculation of A,. The equivalent conductance A, can be obtained from the relationship A~g+[Ag+l Ax-CX-1 A, =
Conductance of AgC1, AgCN, and AgCNS. The conductance data of AgCI, AgCN, and AgCNS do not suggest any simple relationship. On the contrary, it is strongly indicated that these systems involve considerable ion association. The following equilibria are postulated to account for their observed behavior
(9)
A~gzx+[Ag2X+]
+ AA~xZ-CA~L-I
CAgX
(11)
where the X’s indicate the respective ion conductances. On the basis of eq 7a and 7b, eq 11 can be simplified to give
Ki
Ag+X-
ZAgX; AgX
K1 = [AgX]/[Ag+][X-] K 2a
+ Ag+
AgzX+;
K2a = CAg2X+]/[AgX][Ag+] AgX
+ X-
(2)
(3a)
K2b
AgXz-;
K2b = [AgX2-]/[AgX][X-]
(3b)
K3a
[A~~X~]/[A~ZX+][X-]
(48)
Ag2Xz;
K3b CAg2XzI/ CAgx2-I From the charge-neutrality rule
[&+I
[&+I
+ [AgzX+] = [X-I + [AgXz-]
(4b) (5)
Assuming K2a = K2b = Kz,we obtain
+
[Ag+I(l f Kz[AgXI) = [X-](l Kz[AgX]) (6) Thus [Ag+l = [X-I (7%) and (7b) [AgZX+I = [AgX2-] From mass balance, the total concentration CAgX can be expressed as CAgX
[&+I
+ [&XI + 2[Ag2X+l + [&&-I
+ 2[AgzXzl
+
Potentiometry. For a silver salt AgX which as a monomer dissociates according to
Kab
9Ag+
+
+
+ X- =AgzXz; Kaa
&X+
Equation 12 has been used to calculate the conductance of AgCl, AgCN, and AgCNS assuming different trial values of K1, Kz, and K3 for each system until a satisfactory agreement with the observed conductance was obtained. I n all cases, variation of the ion conductances with concentration has been ignored, and the sums A ~ g t AX- and X A ~ ~ X + X A ~ X ~ have been set equal to 80 and 40, respectively. The assumed value of 80 for A ~ g t AX- seems fairly reasonable and compares favorably with the estimates of limiting cond u c t a n c e ~reported ~ for these electrolytes in pyridine.
(8)
AgX (or Ag+X-) Z Z Ag+
+ X-
(13)
the (over-all) dissociation constant, K~gx,can be expressed as KAgx = aAg+aX-/aAgX (14) where a~,+and ax- denote the activities of Ag+ and Xand ~ A represents ~ X the activity of the uncharged species. If it is assumed that the ionic activity coefficients are equal and the activity coefficient of the uncharged species is unity, eq 14 can be rearranged to give aAg+
= dKagx[AgX]
(15)
on the basis of the electroneutrality rule. (4) P. Walden, L. F. Audrieth, and E. J. Birr, 2. Physik. Chem., A160, 337 (1932). Volume 79, Number 9 March 1969
MUKHERJEE, KELLY,RICHARDS, AND LUKACS
582 Furthermore, if K A a is sufficiently small, the equilibrium concentration [AgX] may be replaced by the corX permit the responding analytical concentration C A ~ to rewriting of eq 15 in the form
dKAgxCAgx (16) The expression for the emf of the cell I a t 25" [cell I : Zn(Hg) jZnC12(s) reference electrodel iAgXIAg(s)] is given by aAg+
E=
fl"Agt1Ag
=
- Eref
+ 0.05916 log a~g+
(17)
Substituting eq 16 into eq 17 gives
E = EoAg+lAg
- Ereff 0.02958 log Kagx + 0.02958 log CAgX
(18)
It is evident from eq 18 that in the case of a silver salt which dissociates in the manner shown by eq 13 and X eq 14) a which has a relatively small value of K A ~ (cf. X be a straight line with a slope plot of E vs. log C A ~will of 0.02958 V a t 25". Calculation of E o A g + l A g . I n order to calculate E " A ~ +from ~ A the ~ emf data using eq 17, knowledge of the activity of silver ion for a given concentration of a silver salt is required. Estimates of the equilibrium constants as obtained from conductance measurements are useful in this respect. The total salt concentration corresponding to an arbitrary value of free silver ion concentration can be calculated from eq 10 for the chloride, cyanide, and thiocyanate. I n order to obtain similar relationship for the silver nitrate and picrate the
1.5
1.0
c" 8 -I
0.5
(thermodynamic) dissociation constants of 9.3 X and 3.06 X respectively, derived from the FuossKraus treatrnentj2 on the basis of simple monomeric dissociation, have been used in the expression
CA~X =
[&+I f [Ag+I2fi2/K~g~
(19)
where f i denotes the ionic activity coefficient. Thus, using, when appropriate, eq 10 or 19, together with the Debye-IJiickel limiting law in the form -log
fi
= 8.191&
it is possible to generate values of aAgt corresponding to different values of the total concentrations for each of the silver salts studied. Plots of 0.0591G log aAg+ us. log C A ~ X can then be constructed for comparison X of interest. In the regions with the E vs. log C A ~ plot where the slopes are the same and preferably at concentrations low enough to permit the use of the DebyeHuckel limiting law, the difference between the observed emf, E , for cell I and the calculated value of 0.05916 log U A ~ +for a given total concentration would be a measure of E o A g t I A g - Eref(cf. eq 17). From a knowledge of Eref it is therefore possible finally to calculate EoAg+IAg.
Experimental Section Chemicals. Pyridine was purified, stored, and dispensed according to the procedure described previously.*b Silver nitrate used was of reagent grade. The chloride, cyanide, and thiocyanate were prepared by metathesis using excess silver nitrate and the appropriate potassium salts. Silver picrate was obtained by the reaction of silver nitrate with picric acid and subsequently recrystallization twice from ethanol. Potentiometric Techniques. These have been described Both HglHgClz(s), ZiCl(s), and Zn(Hg) IZnC&(s) reference electrodes proved suitable for use in pyridine solutions. The general procedures for preparing these electrodes have been discussed previously.'I6 The emf values reported in this study are considered reliable to within =k 2 mV. All measurements were made in an air bath maintained at 25 f 0.5".
Results and Discussions
0
I
I
2
4
- LOGcAgx
I 6
Figure 1. Plot of log A, us. -log C A ~ ~ AgCl: . U (exptl), C (calcd K 1 = 1.2 X lo7; K z = 1.6 X 104; K3 = 6.5 X 106); AgCNS: 0 (exptl), (calcd K I = 2.9 X lo5; KZ = 1.0 X lo2; K3 = 0 ) ; AgCN: A (exptl), A (calcd K1 = 7.5 x 106; K~ = 2.0 x 104; K~ = 2.0 x 104). The Journal of Physical Chemistry
Plots of log A. us. -log CAgx for AgC1, AgCN, and AgCNS based on the conductance data of Mathews and Johnson3 are shown in Figure 1. The theoretical plot for each system based on calculations according to eq 12 is also given for comparison. The values of K I , K z , and KBwhich yielded the best fit in individual cases have been given in the legend. The results of potentiometric measurements for the different silver salts are summarized in Figure 2 in the form of E us. -log CAgx plots. As is evident], in all of ( 6 ) S. Bruokenstein and (1960).
L. 11,Mukherjee, J . Phu/s. Chern., 64, 1601
583
EQUILIBRIA IN PYRIDINE
1.20
less linear below dd with curvature developing at high concentrations. Possibly, the curvature may indicate deviation caused by the inapplicability of the Debye-Hiickel limiting lam in calculating activity coefficients a t high concentrations. Table I summarizes
\.
Table I: Standard Potential of the Reaction Ag' + e e Ag(s) in Pyridine
I
5
1
w
I .IO
I.oc
I
- LOGCAg
3
6,
Figure 2. Plot of E vs. -log C A ~ ~ : AgCl; A, AgCh'; 0, AgCNS; 0, AgN03; -0-,Ag(pic) (os. Zn(Hg) ZiiCl~(s) reference electrode); 0 , AgCPu'S; m, AgNOa; -e-, Ag(pic) (us. Hg HgClz (s), LiCl (s) reference electrode). All emf's shown in the figure are referred t o the Zn(Hg) ZnCh (s) reference electrode. (The emf of the cell Zc(Hg) ZnCh (s) reference e1ectrode))LiCl(s), HgCli (s) H g reference electrode is 1.2245 V.)
1
1
I
I
1
I
t
-0.36
CJ -0.30 \ & % + + , / -
8-0.24
-0.18
-
-Log cAgXa
AgCl
3.00 3.50 3.76
1,340 1.341 1.340 Av 1.340 i 0,0003
AgCN
3.50 4.00
1.345 1,343 Av 1.344 =k 0,001
AgCNS
2.50 3.00 3.50
1.338 1.336 1.338 Av 1.337 rt 0.003
AgNOs
3.25 4.00
1.339 1.338 Av 1,338 i 0.0005
Adpic)
3.25 4.00
E O A ~ + I A 5' ~,~
1.338 1.338
Av 1.338 =k 0 a
the present cases the plots are linear over the concentration ranges studied; the avcrage slopes are in the vicinity of 0.02958 V as required by eq 18 except in the case of the nitrate and picrate. The slightly higher slope (-0.047 V) observed in these last two cases is conceivably due to tlzcir relatively greater degrce of dissociation which would invalidate the simplifyiizg assumption made i n deriving eq 16 from eq 15.' I n all cases, the plots of the calculated values of (Figure 3) are more or 0.05916 log CZA& us. -log C A ~ X
AgX
Interpolated values used in comparing plots given in Figures Tis. the Zn(Hg)lZnClz(s) reference electrode.
2 and 3.
the average values of E ' A ~ +ralculatd ~A~ with reference to the different silver salts. The grand average value of Eo*,+ is found to be 1.330 f 0.002 T7 U S , Zn(Hg) I ZnCls(s) reference electrode. I'sing the value of -0.788 V1 for the potential of the Zn(Hg)IZnC12(s) reference electrode zis. nhe, the value of EoAg+lAgis found to be 0.551 V. It may be remarked a t this point that, although the procedure adopted for the treatment of the conductance data of 4gC1, AgCS, and AgCNS is indeed approximate, the generally consistent agreement obtained in the present correlation is significant and provides a verification of the over-all reliability of the trial values of the various parameters, such as K1, K z , etc., and the ion conductances used in the calculations. Furthermore, it should be recognized that, in spite of the fact that all K's as introduced in the treatment of the conductance data are formal constants, the activity coefficient correction for the monomer dissociation into simple ions-the predominant process at low concentrations-is relatively unimportant. Thus, the values of K 1 for AgC1, AgCN, and AgCSS should closely compare with the corresponding thermodynamic values. Based on the present value of K1 our estimate of the X eq 14), for monomeric dissociation constant, K A ~ (cf. AgCl is 8.3 X lo-*. Earlier spectrophotometric Volume 73, ATumber S March 1969
MILTONMANESAND I,.J. E. HOFER
584
studiese of silver chloride solutions in pyridine which yielded a value of 8.4 X for K A ~ con~ the , assumption of simple dissociation only, are not corroborated in the present work.
donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research.
Acknowledgment. Acknowledgment is made to the
(6) S.Bruckenstein and
J. Osugi, J. Phys. Chem., 65,1868(1961).
Application of the Polanyi Adsorption Potential Theory to Adsorption from Solution on Activated Carbon by Milton Manes1&and L. J. E. Hofer’b Mellon Institute, Pittsburgh, Pennsylvania
15813
(Receioed August 8 , 1968)
Liquid-phase adsorption isotherms at 25’ on an activated carbon have been determined, over a wide range of concentrations, for the following systems: Sudan I11 (benzeneazo-p-benzeneazo-&naphthol) in acetone, cyclohexane, carbon tetrachloride, benzene, and carbon disulfide, and Butter Yellow (p-dimethylaminoazobenzene) in methanol, acetonitrile, acetone, 2-propanol, cyclohexane, heptane, benzene, and carbon disulfide. Except for the high capacity range, most of the data can be fitted to a correlation curve determined for the same carbon from gas-phase adsorption measurements, as predicted by the Polanyi adsorption potential theory. The experimental link between liquid and gas-phase adsorption and the relative constancy of the solvent effect, on adsorption (measured in appropriate units) appear to introduce a measure of predictability to at least some liquid-phase adsorption isotherms. Adsorption tends to be weakest in solvents of highest refractive index.
Introduction The Polaiiyi adsorption potential theory2and modifications thereof have been widely applied to gas-phase Ry contrast , application of the theory lo liquid-phase adsorption has been used only in modified form for adsorption of binary liquids8 and apparently not at all for solutes. Since t>henature of the forces 011 adsorbed molecules may be expected to be independent of their state of aggregation, it seemed reasonable to expect that the adsorption isotherms of at least properly chosen solute-solvent systems should conform to a significant degree to the Polanyi theory. Such conformation has been found for the adsorption isotherms of two solutes (Sudan I11 and p-dimethylaminoazobenzene) in a wide variety of solvents. The results provide the expected experimental link between gas-phase and liquid-phase adsorption on activated carbon and, to the extent that they will be confirmed by continuing work, introduce the possibility of predicting adsorption isotherms on activated carbons for a wide variety of systems from minimal data.
Theoretical Section The Polanyi adsorption potential theory for gases may be summarized as follows: within the range of the The Journal o/ Physical Chemistry
attractive forces of the fiolid surface (the “adsorption space”) the potential energy of a given gas is reduced, relative to its value at infinity, by an amount e (the adsorption potential) that for a given gas depends on proximity to the solid surface. Onc can imagine points of equal e t o be joined to form equipotential surfaces that together with the solid surface enclose a volume ~ ( t ) . The plot of ~ ( e ) against E (the “characteristic curve”) depends on the structure of the adsorbent, and no attempt is made to derive it from theory; it is independent of temperature. When the adsorbent, initially under vacuum, is exposed to increasing pressures of gas, (1) (a) Professor, Department of Chemistry, Kent State University, Kent, Ohio: (b) Head, Adsorption Fellowship (Sponsored by Pittsburgh Activated Carbon Division of the Calgon Corporation) Rlellon Institute, Carnegie-Mellon University, Pit,tsburgli, Pa. (2) (a) M.Polanyi, Verh. Deut. Physik. Ges., 16, 1012 (1914): 18, 55 (1916): Z . Elektrochem., 26, 370 (1920); (b) M. Polanyi, Z . Physik, 2 , 111 (1920). (3) M.M.Dubinin, Chem. Rev., 60, 235 (1960). (4) W. K. Lewis, E. R . Gilliland, B. Chertow, and W. P. Cadogan, I n d . Eng. Chein., 42, 1319 (1950). (5) R. J. Grant, 31. Manes, and S. B. Smith, A . 1 . C h . E . J., 8 , 403 (19G2). (6) R. J. Grant and M. Manes, I n d . Eng. Chem. Fundamentals. 3 , 221 (1964). (7) R.J. Grant and M. Manes, ibid., 5, 490 (1966). (8) R. S. Hansen and W. V. Fackler, J . P h y s . Chein., 57, 634 (1053).
